# Statistical Concepts of ANOVA, Samples, Chi-square, and Regression Equation

I need help answering these questions:

e. Why is the F-distribution important? How do you determine if a significant difference exists among the groups in ANOVA? How do you determine differences between the groups in ANOVA? Provide an ANOVA example using either a personal or professional experience.

f. What is an independent sample and what is a related sample? When should researchers use varying hypothesis tests for the different types of samples? Is one sample more appropriate to use than the other? Give an example of independent and related sample that can be used in your organization.

g. Why would you use the chi-square statistic? What type of data is used with chi-square analysis? Provide an explanation of a chi-square test of homogeneity and a chi-square test of independence.

h. When is a regression equation used? What terms describe the fit of a regression equation to the data? What is the importance of the coefficient of determination (r2)?

#### Solution Preview

e. Why is the F-distribution important? How do you determine if a significant difference exists among the groups in ANOVA? How do you determine differences between the groups in ANOVA? Provide an ANOVA example using either a personal or professional experience.

F distribution is a distribution that is of great importance to test the significance of estimated mean square in an analysis of variance and in regression analysis.

When P value for F test is less than 0.05, we could conclude that a significant difference exists among the groups.

For example, we have three brands of cars and their MPG are:

A B C

40 30 35

38 29 36

39 28 28

38.5 27 27

37 26 37

After running "ANOVA: single factor", we could obtain the following output:

Anova: Single Factor

SUMMARY

Groups Count Sum Average Variance

A 5 192.5 38.5 1.25

B 5 140 28 2.5

C 5 163 32.6 22.3

ANOVA

Source of Variation SS df MS F P-value F crit

Between Groups 277.0333 2 138.5167 15.95202 0.000417 3.885294

Within Groups 104.2 12 8.683333

Total 381.2333 14

Null hypothesis: Mean MPG(A)=mean MPG(B)=mean MPG(C)

Alternative hypothesis: at least two of them are significantly different.

Since P value for F test is 0.000417, less than 0.05, we reject Ho and ...

#### Solution Summary

The statistical concepts of ANOVA, samples, chi-square and regression equations are provided.